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Commentarii Mathematici Helvetici


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Volume 90, Issue 1, 2015, pp. 59–74
DOI: 10.4171/CMH/346

Published online: 2015-02-23

On Schoen surfaces

Ciro Ciliberto[1], Margarida Mendes Lopes[2] and Xavier Roulleau[3]

(1) Università di Roma, Italy
(2) Instituto Superior Técnico, Lisboa, Portugal
(3) Université de Poitiers, Futuroscope Chasseneuil, France

We give a new construction of the irregular surfaces of general type with $p_g=5, \chi=2, K^ 2=8$,recently discovered by C. Schoen in [24]. Our approach proves that, if $S$ is a general Schoen surface, its canonical map is a finite morphism of degree 2 onto a canonical surface with invariants $p_{g}=5, \chi=6, \, K^{2}=8$, a complete intersection of a quadric and a quartic hypersurface in $\mathbb P^{4}$, with 40 even nodes.

Keywords: Irregular surfaces, Lagrangian surfaces, deformations of surfaces, canonical maps

Ciliberto Ciro, Mendes Lopes Margarida, Roulleau Xavier: On Schoen surfaces. Comment. Math. Helv. 90 (2015), 59-74. doi: 10.4171/CMH/346